Subgroups — C₁₁×#17936 #14595129

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3103	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1592	C₂	1	4	yes	maximal, complemented
5	C₁₁×#1585	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1571	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1480	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#131	—	2	1	no	—
11	C₁₁×#532	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#481	C₄	1	2	yes	—
14	C₁₁×#475	C₄	1	2	yes	—
15	C₁₁×#460	C₄	1	2	yes	—
16	C₁₁×#448	C₄	1	2	yes	—
17	C₁₁×#446	—	2	1	no	—
18	C₁₁×#446	—	2	1	no	—
19	C₁₁×#446	C₂²	1	2	yes	—
20	C₁₁×#446	C₂²	1	2	yes	—
21	C₄×C₁₁×SD₁₆	C₂²	1	4	yes	—
22	C₁₁×#436	—	2	1	no	—
23	C₁₁×#436	C₂²	1	2	yes	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₈×D₄×C₁₁	C₂²	1	2	yes	—
26	C₁₁×#431	C₂²	1	1	yes	characteristic
27	C₁₁×#431	C₂²	1	1	yes	characteristic
28	C₁₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₁×#408	—	2	1	no	—
32	C₂×C₁₁×#97	—	2	1	no	—
33	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₁₁×#335	C₂²	1	4	yes	—
35	C₁₁×Q₈⋊C₈	C₂²	1	4	yes	—
36	C₁₁×D₄⋊C₈	C₂²	1	4	yes	—
37	C₁₁×#322	C₂²	1	2	yes	—
38	C₁₁×#322	C₂²	1	2	yes	—
39	C₂×C₁₁×#41	—	2	1	no	—
40	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
42	C₁₁×#131	—	4	4	no	—
43	C₂×C₁₁×M₁₆	—	2	1	no	—
44	C₂×C₁₁×M₁₆	—	2	2	no	—
45	C₂²×C₈×C₁₁	—	2	1	no	—
46	C₂²×C₈×C₁₁	—	2	2	no	—
47	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
51	C₁₁×#124	—	2	1	no	—
52	C₁₁×#121	—	2	1	no	—
53	C₁₁×#121	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₁₁	—	2	1	no	—
55	C₄×Q₈×C₁₁	—	2	1	no	—
56	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
58	C₄×D₄×C₁₁	—	2	1	no	—
59	C₄×D₄×C₁₁	C₂³	1	2	yes	—
60	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	—	2	1	no	—
63	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×#106	C₂×C₄	1	4	yes	—
65	C₁₁×C₄⋊C₈	—	2	2	no	—
66	C₁₁×C₄⋊C₈	—	2	2	no	—
67	C₁₁×C₄⋊C₈	—	2	1	no	—
68	C₁₁×C₄⋊C₈	—	2	1	no	—
69	C₁₁×C₄⋊C₈	—	2	1	no	—
70	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
72	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₁×#103	C₂×C₄	1	4	yes	—
74	C₁₁×#102	C₂×C₄	1	4	yes	—
75	C₁₁×C₂²⋊C₈	—	2	1	no	—
76	C₁₁×C₂²⋊C₈	—	2	2	no	—
77	C₁₁×C₂²⋊C₈	—	2	2	no	—
78	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
79	C₁₁×#97	—	2	2	no	—
80	C₁₁×#97	—	2	2	no	—
81	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₁	C₂³	1	2	yes	—
84	C₄×C₈×C₁₁	C₂³	1	2	yes	—
85	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
87	#17936	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₁₁×#41	—	4	2	no	—
89	C₁₁×#41	—	4	2	no	—
90	C₂×Q₈×C₁₁	—	2	1	no	—
91	C₂×Q₈×C₁₁	—	2	1	no	—
92	C₂×Q₈×C₁₁	—	4	2	no	—
93	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	—	2	1	no	—
96	C₂×D₄×C₁₁	—	2	1	no	—
97	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	—	2	1	no	—
99	C₂²×C₄×C₁₁	—	2	1	no	—
100	C₂²×C₄×C₁₁	—	2	2	no	—
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
104	C₁₁×SD₁₆	—	4	4	no	—
105	C₁₁×M₁₆	—	4	4	no	—
106	C₁₁×M₁₆	—	4	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	4	4	no	—
113	C₂×C₈×C₁₁	—	4	2	no	—
114	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₁₁×C₄⋊C₄	—	2	2	no	—
120	C₁₁×C₄⋊C₄	—	2	1	no	—
121	C₁₁×C₄⋊C₄	—	2	1	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
124	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
125	C₁₁×C₂²⋊C₄	—	2	2	no	—
126	C₁₁×C₂²⋊C₄	—	2	2	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₁	#41	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
133	#3103	C₂×C₁₁	1	1	yes	characteristic
134	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
135	#2931	C₂×C₁₁	1	1	yes	characteristic
136	#1592	C₂×C₁₁	1	4	yes	complemented
137	#1585	C₂×C₁₁	1	4	yes	complemented
138	#1571	C₂×C₁₁	1	1	yes	characteristic, complemented
139	#1487	C₂×C₁₁	1	1	yes	characteristic, complemented
140	#1480	C₂×C₁₁	1	1	yes	characteristic
141	#1452	C₂×C₁₁	1	1	yes	characteristic, complemented
142	C₂³×C₁₁	—	2	2	no	—
143	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₁₁	—	2	2	no	—
145	Q₈×C₁₁	—	2	2	no	—
146	Q₈×C₁₁	—	4	2	no	—
147	Q₈×C₁₁	—	4	2	no	—
148	D₄×C₁₁	—	2	4	no	—
149	D₄×C₁₁	—	4	2	no	—
150	D₄×C₁₁	—	4	4	no	—
151	D₄×C₁₁	—	4	2	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	4	1	no	—
157	C₂×C₄×C₁₁	—	4	2	no	—
158	C₂×C₄×C₁₁	—	4	2	no	—
159	C₂×C₄×C₁₁	—	4	2	no	—
160	C₂×C₄×C₁₁	—	4	2	no	—
161	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₁	#137	1	2	yes	—
166	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
169	C₈×C₁₁	—	2	4	no	—
170	C₈×C₁₁	—	2	1	no	—
171	C₈×C₁₁	—	2	1	no	—
172	C₈×C₁₁	—	2	1	no	—
173	C₈×C₁₁	—	2	1	no	—
174	C₈×C₁₁	—	4	2	no	—
175	C₈×C₁₁	—	4	2	no	—
176	C₈×C₁₁	—	4	2	no	—
177	C₂×#131	—	2	1	no	—
178	#532	C₂²×C₁₁	1	1	yes	characteristic
179	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
180	#481	C₄×C₁₁	1	2	yes	—
181	#475	C₄×C₁₁	1	2	yes	—
182	#460	C₄×C₁₁	1	2	yes	—
183	#448	C₄×C₁₁	1	2	yes	—
184	#446	—	2	1	no	—
185	#446	—	2	1	no	—
186	#446	C₂²×C₁₁	1	2	yes	—
187	#446	C₂²×C₁₁	1	2	yes	—
188	C₄×SD₁₆	C₂²×C₁₁	1	4	yes	—
189	#436	—	2	1	no	—
190	#436	C₂²×C₁₁	1	2	yes	—
191	C₈×D₄	—	2	1	no	—
192	C₈×D₄	C₂²×C₁₁	1	2	yes	—
193	#431	C₂²×C₁₁	1	1	yes	characteristic
194	#431	C₂²×C₁₁	1	1	yes	characteristic
195	#423	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×C₄⋊C₈	—	2	1	no	—
197	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
198	#408	—	2	1	no	—
199	C₂×#97	—	2	1	no	—
200	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
201	#335	C₂²×C₁₁	1	4	yes	—
202	Q₈⋊C₈	C₂²×C₁₁	1	4	yes	—
203	D₄⋊C₈	C₂²×C₁₁	1	4	yes	—
204	#322	C₂²×C₁₁	1	2	yes	—
205	#322	C₂²×C₁₁	1	2	yes	—
206	C₂²×C₁₁	—	2	1	no	—
207	C₂²×C₁₁	—	2	1	no	—
208	C₂²×C₁₁	—	4	2	no	—
209	C₂²×C₁₁	—	4	2	no	—
210	C₂²×C₁₁	—	4	2	no	—
211	C₂²×C₁₁	#440	1	2	yes	—
212	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₁₁	—	2	1	no	—
214	C₄×C₁₁	—	2	1	no	—
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	—	4	2	no	—
217	C₄×C₁₁	—	4	2	no	—
218	C₄×C₁₁	—	4	2	no	—
219	C₄×C₁₁	#440	1	2	yes	—
220	C₄×C₁₁	#568	1	2	yes	—
221	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
223	C₂×#41	—	2	1	no	—
224	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
225	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
226	#131	—	4	4	no	—
227	C₂×M₁₆	—	2	1	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
234	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
235	#124	—	2	1	no	—
236	#121	—	2	1	no	—
237	#121	C₂×C₄×C₁₁	1	2	yes	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂×C₄×C₁₁	1	2	yes	—
241	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	C₂³×C₁₁	1	2	yes	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
248	#106	C₂×C₄×C₁₁	1	4	yes	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
255	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
256	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
257	#103	C₂×C₄×C₁₁	1	4	yes	—
258	#102	C₂×C₄×C₁₁	1	4	yes	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
263	#97	—	2	2	no	—
264	#97	—	2	2	no	—
265	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
266	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₁₁	1	2	yes	—
268	C₄×C₈	C₂³×C₁₁	1	2	yes	—
269	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
271	C₂×C₁₁	—	2	2	no	—
272	C₂×C₁₁	—	8	2	no	—
273	C₂×C₁₁	#2930	1	1	yes	characteristic
274	C₂×C₁₁	C₂×#440	1	1	yes	characteristic
275	C₂×C₁₁	#2955	1	1	yes	characteristic
276	#41	—	4	2	no	—
277	#41	—	4	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
292	SD₁₆	—	4	4	no	—
293	M₁₆	—	4	4	no	—
294	M₁₆	—	4	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
303	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
312	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
318	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
319	C₄²	C₁₁×#41	1	1	yes	characteristic
320	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
321	C₁₁	#17936	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³	—	2	2	no	—
323	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
324	Q₈	—	2	2	no	—
325	Q₈	—	2	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	D₄	—	2	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	4	no	—
331	D₄	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
343	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
344	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
345	C₂×C₄	C₁₁×#137	1	2	yes	—
346	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
348	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
349	C₈	—	2	4	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	C₁₁×#440	1	2	yes	—
363	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	C₁₁×#440	1	2	yes	—
371	C₄	C₁₁×#568	1	2	yes	—
372	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
373	C₄	C₂×C₁₁×#137	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	8	2	no	—
376	C₂	C₁₁×#2930	1	1	yes	characteristic
377	C₂	C₂×C₁₁×#440	1	1	yes	characteristic
378	C₂	C₁₁×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1592	C₂	semidirect
5. C₁₁×#1585	C₂	semidirect
6. C₁₁×#1571	C₂	semidirect
7. C₁₁×#1487	C₂	semidirect
9. C₁₁×#1452	C₂	semidirect
87. #17936	C₁₁	direct (N × H)
134. C₂×#446	C₂×C₁₁	semidirect
136. #1592	C₂×C₁₁	semidirect
137. #1585	C₂×C₁₁	semidirect
138. #1571	C₂×C₁₁	semidirect
139. #1487	C₂×C₁₁	semidirect
141. #1452	C₂×C₁₁	semidirect
321. C₁₁	#17936	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₁×#3103	2
C₂×C₁₁×#446	2
C₁₁×#2931	2
C₁₁×#1592	2
C₁₁×#1585	2
C₁₁×#1571	2
C₁₁×#1487	2
C₁₁×#1480	2
C₁₁×#1452	2
#17936	11

Subgroups — C11×#17936 #14595129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17936 #14595129